calculating trig values

[carebear]

sin(2pi/3)sec(-pi/6) - tan(25pi/4)csc(11pi/6)

I get the answer to be 3. Is that correct?

 

[tkhunny]

How did you get that. Let's see the path by which you arrived at this result.

\(\displaystyle \sin\left(\frac{2\pi}{3}\right) = \frac{\sqrt{3}}{2}\)

What else?

 

[soroban]

Hello, carebear!

\(\displaystyle \sin\left(\frac{2\pi}{3}\right)\sec\left(-\frac{\pi}{6}\right) - \tan\left(\frac{25\pi}{4}\right)\csc\left(\frac{11\pi}{6}\right)\)

I get the answer to be 3 . . . Is that correct? . . . . Yes!

\(\displaystyle \sin\left(\frac{2\pi}{3}\right)\sec\left(-\frac{\pi}{6}\right) - \tan\left(\frac{25\pi}{4}\right) \cos\left(\frac{11\pi}{6}\right)\)

. . \(\displaystyle =\;\;\left(\frac{\sqrt{3}}{2}\right)\left(\frac{2}{\sqrt{3}}\right) - \bigg(1\bigg)\bigg(-2\bigg) \;\;=\;\; 1 - (-2) \;\;=\;\;3\)

.